Why is the denominator ignored in the Bayes' rule?
The answer from @kiner_shah in the comments has solved it:


  They have eliminated it because in comparing probability for best outcome, it would just introduce additional division and the divisor p(x) is same for all candidates. For example, if I tell you to compare the largest of the following numbers: 3/2, 5/2, 1/2, you will without thinking pick 5/2 since the divisors are same and 5 is greatest of all.